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Created By
Abhishek
Class-10
Roll No-03
Linear Equations
Definition of a Linear Equation
A linear equation in two variable x is an equation
that can be written in...
A pair of linear equations
in two variables can be
solved by the:
(i) Graphically method
(ii) Algebraic method
GRAPHICAL SOLUTIONS OF A
LINEAR EQUATION
Let us consider the following system of
two simultaneous linear equations in
two ...
xxx

00
Types of Solutions of Systems of
Equations
• One solution – the lines cross at one point

• No solution – the lines do not...
Algebraic method
TO SOLVE A PAIR
OF LINEAR
EQUATION IN TWO
VARIABLE
To solve a pair of linear equations in
two variables algebraically, we have
following methods:(i) Substitution method
(ii)...
SUBSTITUTION METHOD
STEPS
Obtain the two equations. Let the equations be
a1x + b1y + c1 = 0 ----------- (i)
a2x + b2y + c2...
Solve the equation obtained in the
previous step to get the value of x.
Substitute the value of x and get
the value of y.
...
x + 2y = -1
x = -2y -1 ------- (iii)
Substituting the value of x in
equation (ii), we get
2x – 3y = 12
2 ( -2y – 1) – 3y =...
Putting the value of y in eq. (iii), we get
x = - 2y -1
x = - 2 x (-2) – 1
=4–1
=3
Hence the solution of the equation
is
(...
ELIMINATION METHOD
• In this method, we eliminate one of the

two variables to obtain an equation in one
variable which ca...
Let 3x + 2y = 11 --------- (i)
2x + 3y = 4 ---------(ii)
Multiply 3 in equation (i) and 2 in equation
(ii) and subtracting...
• putting the value of X in equation (ii) we

get,
2x + 3y = 4
2 x 5 + 3y = 4
10 + 3y = 4
3y = 4 – 10
3y = - 6
y=-2
Hence,...
CROSS MULTIPLICATION
METHOD
LINEAR EQUATION  IN  TWO VARIABLES PPT
LINEAR EQUATION  IN  TWO VARIABLES PPT
LINEAR EQUATION  IN  TWO VARIABLES PPT
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LINEAR EQUATION IN TWO VARIABLES PPT

It is from the chapter LINEAR EQUATION IN TWO VARIABLES of maths of class 10th.

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LINEAR EQUATION IN TWO VARIABLES PPT

  1. 1. Created By Abhishek Class-10 Roll No-03
  2. 2. Linear Equations Definition of a Linear Equation A linear equation in two variable x is an equation that can be written in the form ax + by + c = 0, where a ,b and c are real numbers and a and b is not equal to 0. An example of a linear equation in x is 2x – 3y + 4 = 0.
  3. 3. A pair of linear equations in two variables can be solved by the: (i) Graphically method (ii) Algebraic method
  4. 4. GRAPHICAL SOLUTIONS OF A LINEAR EQUATION Let us consider the following system of two simultaneous linear equations in two variable. 2x – y = -1 3x + 2y = 9 Here we assign any value to one of the two variables and then determine the value of the other variable from the given equation.
  5. 5. xxx 00
  6. 6. Types of Solutions of Systems of Equations • One solution – the lines cross at one point • No solution – the lines do not cross • Infinitely many solutions – the lines coincide
  7. 7. Algebraic method TO SOLVE A PAIR OF LINEAR EQUATION IN TWO VARIABLE
  8. 8. To solve a pair of linear equations in two variables algebraically, we have following methods:(i) Substitution method (ii) Elimination method (iii) Cross-multiplication method
  9. 9. SUBSTITUTION METHOD STEPS Obtain the two equations. Let the equations be a1x + b1y + c1 = 0 ----------- (i) a2x + b2y + c2 = 0 ----------- (ii) Choose either of the two equations, say (i) and find the value of one variable , say ‘y’ in terms of x Substitute the value of y, obtained in the previous step in equation (ii) to get an equation in x
  10. 10. Solve the equation obtained in the previous step to get the value of x. Substitute the value of x and get the value of y. Let us take an example x + 2y = -1 ------------------ (i) 2x – 3y = 12 -----------------(ii)
  11. 11. x + 2y = -1 x = -2y -1 ------- (iii) Substituting the value of x in equation (ii), we get 2x – 3y = 12 2 ( -2y – 1) – 3y = 12 - 4y – 2 – 3y = 12 - 7y = 14 ; y = -2 ,
  12. 12. Putting the value of y in eq. (iii), we get x = - 2y -1 x = - 2 x (-2) – 1 =4–1 =3 Hence the solution of the equation is ( 3, - 2 )
  13. 13. ELIMINATION METHOD • In this method, we eliminate one of the two variables to obtain an equation in one variable which can easily be solved. Putting the value of this variable in any of the given equations, the value of the other variable can be obtained. • For example: we want to solve, 3x + 2y = 11 2x + 3y = 4
  14. 14. Let 3x + 2y = 11 --------- (i) 2x + 3y = 4 ---------(ii) Multiply 3 in equation (i) and 2 in equation (ii) and subtracting eq iv from iii, we get 9x + 6y = 33 ------ (iii) 4x + 6y = 8 ------- (iv) 5x = 25 x=5
  15. 15. • putting the value of X in equation (ii) we get, 2x + 3y = 4 2 x 5 + 3y = 4 10 + 3y = 4 3y = 4 – 10 3y = - 6 y=-2 Hence, x = 5 and y = -2
  16. 16. CROSS MULTIPLICATION METHOD

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